Coroner David Roberts is reported as saying, “Paul Worthington assaulted his daughter Poppi, in his bed, laid a cover over her and went to sleep.
He said she died because her ability to breathe was compromised as a result of “an unsafe sleeping environment.”
Mr Roberts said her father’s account of events did not “stand up to scrutiny”.
During the three-week inquest at Kendal Coroner’s Court, Poppi, who was 13 months old at the time, father declined to answer 252 questions relating to the circumstances surrounding her death on 12 December 2012.
He said he rushed downstairs and Poppi’s mother, who was asleep there, called an ambulance.
Having heard contradictory evidence from expert medical witnesses, Mr Roberts said he believed Mr Worthington penetrated Poppi’s anus, probably with a finger, and the assault stopped when the youngster cried out in pain.
Mr Worthington has denied any wrongdoing and has not been charged with any offence, with the Crown Prosecution Service saying there is insufficient evidence.